Question

what is the slope of the line represented by the equation $y = -\frac{1}{2}x + \frac{1}{4}$?
$\circ\\ \frac{1}{2}$
$\circ\\ \frac{1}{4}$
$\circ\\ \frac{1}{4}$
$\circ\\ \frac{1}{2}$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Identify the slope from the given equation

In the equation $y=-\frac{1}{2}x+\frac{1}{4}$, comparing it with $y = mx + b$, we can see that $m =-\frac{1}{2}$. But looking at the options, the first option is $\frac{1}{2}$ (probably a typo in the option presentation, and the intended slope is $-\frac{1}{2}$, but among the given options, the first one is $\frac{1}{2}$ which is the coefficient of $x$ in magnitude). Wait, no, the equation is $y =-\frac{1}{2}x+\frac{1}{4}$, so the slope $m=-\frac{1}{2}$. But looking at the options, the first option is $\boldsymbol{\frac{1}{2}}$ (maybe a formatting error in the option's sign, but following the given options, the slope is the coefficient of $x$, so the slope is $-\frac{1}{2}$, but among the options, the first one is $\frac{1}{2}$ which is the coefficient of $x$ in the equation (ignoring the sign error in the option display? Wait, no, the first option is $\frac{1}{2}$? Wait, no, the first option is $\boldsymbol{-\frac{1}{2}}$? Wait, the user's image: the first option is $\frac{1}{2}$ with a negative? Wait, the user's image shows the first option as $\boldsymbol{-\frac{1}{2}}$? Wait, the user's text: "What is the slope of the line represented by the equation $y =-\frac{1}{2}x+\frac{1}{4}$? Options: $\frac{1}{2}$ (with a negative?), $\frac{1}{4}$ (negative), $\frac{1}{4}$, $\frac{1}{2}$". Wait, maybe the first option is $-\frac{1}{2}$. So the slope - intercept form is $y = mx + b$, where $m$ is the slope. So in $y=-\frac{1}{2}x+\frac{1}{4}$, $m =-\frac{1}{2}$, which should be the first option.

Answer:

A. $-\frac{1}{2}$